Olympiad Questions – Algebraic Expressions – Class VII

If x + y = 5, y + z = 7, z + x = 12, what is the value of x + y + z ?

What is the difference between 3a + 2b and -2a – 5b ?

What is the perimeter in cm of the triangle ?

By how much is \( x^{4} – 4x^{2}y^{2} + y^{4}\) less than \( x^{4} + 8x^{2}y^{2} + y^{4}\) ?

Simplify x(y – z) – y(z – x) – z(x – y) .

What is the sum of \( 3y^{2} + 5yz , -2y^{2} -2yz – z^{2} \ and \ -yz + 2z^{2}\)?

Evaluate p – (p – q)- q – (q – p).

If \( p + \dfrac{5}{4}(4 – 2p) = – 4 \) then ,find p ?

A basket has 23 oranges and bananas. How many bananas are there in the basket if there are ‘p’ oranges in it ?

The length of a rectangle is 2(x + 6)cm and its width is half of its length. What is its perimeter ?

What must be added to \( 12x^{3} – 4x^{2} + 3x -7\) to make the sum \( x^{3} + 2x^{3} – 3x + 3\) ?

If P = \( 7x^{2} + 5xy – 9y^{2},\ Q = 4y^{2} – 3x^{2} – 6xy,\ and \ R = -4x^{2} + xy + 5y^{2}\). So P + Q + R = ?

Simplify 2x – { 5y – (x- 2y)}.

Simplify – a – [a + { a + b – 2a – (a – 2b) } – b]

Simplify 2x – 3y – [3x – 2y – {x – z – (x – 2y)}]

The coefficient of x in \( \dfrac{-5}{2}xyz^{2}\) is

If x = 1, and y =2, find the value of 3x – 5y .

Find the value of \(a^{2} + b^{2} + 2ab\) for a = 1, b = 2.

Evaluate \( \dfrac{x}{y} + \dfrac{y}{z} + \dfrac{z}{x}\) for x = -2, y = -1, z = 3.

The value of \( \dfrac{n(n+1)(2n+1)}{6}\) at n = 5 is

If \(\dfrac{5x – 4}{6x – 4} = \dfrac{4}{5}\) then, x = ?

Add \( 5x^{2} + 7x – 6z^{2}, 4y+3x^{2} , 9x^{2} + 2z^{2} – 9y,\ and \ 2y – 2x^{2} \)

Subtract \( x^{2} + y^{2} + 3xy\) from \(4x^{2} + 2xy – 3y^{2}\)

How much is \(x^{2} – 2xy + 3y^{2}\) less than \(2x^{2} – 3y^{2} + xy \) ?

Find the value of \(4(a^{2} + b^{2} + 2ab) – [4(a^{2} + b^{2} + 2ab) – {-b^{3} + 4(a – 3)}] \) whwn a = 3, b = 1.

Simplify 2x – [3y – {2x – (y -x)}]

Subtract \( 2 + p^{2} + 3pq + q^{2} \) from \(1 + 3p^{2} – 2pq – 3q^{2}\)

The value of (2x + 3y) + (2x – 3y) is

If x + y = 2z then find the value of \(\dfrac{x}{x-z} + \dfrac{z}{y – z}\)

If \( x + \dfrac{1}{x} = 2 \) then \(x^{2} + \dfrac{1}{x^{2}} = \)?